关于完全数据的推理
On Inferences from Completed Data
摘要：
矩阵补全已经成为一种非常重要的技术，因为数据科学家经常面对他们希望执行统计推断的大型不完整数据集。我们研究如何通过矩阵补全引入的错误影响统计推断。此外，我们证明了恢复误差界取决于几个常见的统计推断的矩阵恢复误差。我们认为矩阵恢复通过核范数最小化和一个变种，$\ell_1$正则化核范数最小化的数据与结构化的采样模式。最后，我们运行了一系列的数值实验的合成数据和真实的病人调查MyLymeData，说明推理恢复误差和矩阵恢复误差之间的关系。这些结果表明，精确的矩阵恢复往往是不必要的，以实现小的推理恢复误差。
英文摘要：
Matrix completion has become an extremely important technique as data scientists are routinely faced with large, incomplete datasets on which they wish to perform statistical inferences. We investigate how error introduced via matrix completion affects statistical inference. Furthermore, we prove recovery error bounds which depend upon the matrix recovery error for several common statistical inferences. We consider matrix recovery via nuclear norm minimization and a variant, $\ell_1$-regularized nuclear norm minimization for data with a structured sampling pattern. Finally, we run a series of numerical experiments on synthetic data and real patient surveys from MyLymeData, which illustrate the relationship between inference recovery error and matrix recovery error. These results indicate that exact matrix recovery is often not necessary to achieve small inference recovery error.
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